Yes, Shabbir I know I need to access SMTP server ,I would like to know if there is some api or log that is accessible and I can use those in my application.
Say when next time application runs it should be able to find the details of failed delivery.
Can any one suggest some such log or api ?Please!

Mostly, when such failure occurs, the From Email address receives a mail from the smtp server with the message. So you will have to monitor the From Email address mail box to find out if such scenario happens.

Check this link http://www.codeproject.com/KB/IP/despop3client.aspx , it has the necessary example code which tells you how you can connect to a pop3 mail box and read its contents. You can use this logic to loop thru each mail items to check if there is a mail item which is realted to the "mail box full" message.